I'm not saying humanity is impossible to describe (on the contrary!). your physics example is too different to what happens in social sciences, it's not a good analogy. you can largely control the conditions under which you throw the balls, while if you're, for instance, studying the recent socio political events in the USA, things are given and then you need to rely on similar past event to understand current ones. even in fields like psychology it's too difficult to even measure initial conditions and outputs. that's why you rely on qualitative analysis.
I agree with what you say, but that doesn't make social sciences the same as astrology. their conclusions, even if qualitative, can be valid and useful.
The problem is that there are no two equal situations in social sciences, so you won't ever have the same set of initial conditions. I don't know why they call them sciences, but the scientific method is intrinsically incompatible with social phenomena.
I agree that a lot of people speak two languages. But man, I've lived in several countries in Europe for many years, and even the average university student doesn't really speak English (and I work at the university so I interact with many of them). Even in countries like Belgium where there're three official languages!
However, I'd agree with that the average educated person can somewhat communicate ideas in a second language. This is what polls usually show, around 30% to 50% of people.
This is obviously not true. You don't have to do the math to realize: when you pay rent, every moth, an important part of your salary simply disappears, leaving nothing for the future. When you pay a mortgage, your paying the house you'll own. Of course, there are interests and fees and whatnot, but you'd need to pay huge amounts so that it becomes unviable; I can't imagine a single scenario where that occurs.
Even if not all LLMs are equal, almost all of them are based on the same base model: transformers. So the general idea is always the same: predict the next token. It becomes more obvious when you try to use LLMs to solve things that you can't find in internet (even if they're simple).
And the testing does not always work. You can be sure that only 80% of the time it will be really really correct, and that forces you to check everything. Of course, using LLMs makes you faster for some tasks, and the fact that they are able to do so much is super impressive, but that's it.
This is where one can notice that LLM are, after all, just stochastic parrots. If we don't have a reliable way to systematically test their outputs, I don't see many jobs being replaced by AI either.
Irrational rotations of a torus are uniformly distributed and closely resemble the image from the blog. The images you linked, on the other hand, are random sequences with positive entropy (which are also uniformly distributed). Confusing these two things is what happens when someone without the necessary expertise tries to sound smart.
Peer review is important for checking the correctness of the results, among other things. It's not uncommon to find big errors; small mistakes are everywhere.
That's a highly biased opinion. The Newtonian conception of physics is trivial for us, and we can say that most people could come up with the ideas by their own, but that's because our world conception is based on those ideas; it's already implicit in how we understand the world. That's why Newton was so important, there was a shift in the whole conceptualization of the physical world. With Maxwell's equations is similar. The interpretation as waves, the fact that the equations are Lorentz symmetric but no Newton symmetric, etc. All that is free for us, and it is not obvious at all.
That's how it works in most scientific fields. If you want more granularity, you check the order of the authors. Sometimes, they explaine in the paper who did what.
Switzerland has just 8 million people, which are divided into two big language groups. And most people speak (or at least understand) English. So, it's natural for the algorithm to converge to content in English.
It says that the underlying action is on the torus (R/Z)^2. If the entries of the matrix are not integers, do we have a well defined action on the torus? It seems to me that the answer is no because Z^2 would not be invariant by the action.
In the case of Mandelbrot, there is a self similar renormalization process, so you can obtain such a formula. For the "fixed points" of the renormalization process, the formula is super simple; for other points, you might need more computations, but it's nevertheless an efficient method. There is a paper of Bartholdi where he explains this in terms of automata.
How is AI different from using a calculator? AI is just giving a new abstraction layer, in the same way that computers have done before AI. And these non-AI tools have allowed us to produce both deep research and beautiful theories.
I'd be more worried about the problems related to a few companies concentrating all the tools and therefore the power.